International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol XXXV, Part B2. Istanbul 2004
where s represent sub-band images, acquired from
stationary wavelet transform.
4. Updating the membership matrix U.
, 7-1
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À
5. Stopif UT! — UU < e , otherwise increase t and go
to step 3.
The FCM algorithm is proved to be very well suitable for
remote sensing image segmentation. But at the same time it
exhibits sensitivity to the initial guess with regard to both speed
and stability and also shows sensitivity to noise.
Figure 4 and 7 are the two- and three-region classification
results for the images in Figure 4 using this FCM method.
2.3 Decision Trees
Another common approach to classification is to use decision
trees. The decision tree itself is a set of decision rules that
describe each group's patterns learned from these given
examples.
The decision tree algorithm used here is the "Quick, Unbiased,
Efficient Statistical Trees" (QUEST). The algorithm is
described in [16] and the performance of this algorithm
compared with other classification methods can be found in
[17].
Applying the QUEST to the original images in Figure 4 to
discriminate regions of land and water, Figure 5 gives the
classification results. The three-region results are plotted in
Figure 8.
We must note before applying the above classification
techniques, denoising method should be applied to the original
images. In this paper, we use the wavelet denoising method
combined with simple nonlinear speckle reduction filters (i.e.
median filters). At first we apply median filtering to the original
images. Median filtering is a widely used nonlinear process
useful in reducing impulses, or salt-and-pepper noise. It is also
useful in preserving edges in an image while reducing random
noise. The wavelet denoising method is then applied. Wavelet
transform is a useful tool for the time-frequency analysis of
signals. From the viewpoint of signal processing, wavelet
analysis represents a signal by its components in a series of
independent frequency channels (scales). By analyzing the
behavior of the signal in each scale, we can find the features of
the signal or discriminate different parts (such as the noise and
the useful signal) of the combined signal. Mallat's [11] research
indicated that the local maximums of the wavelet transform of
noise and signal have different variation rules with the change
of the scale. So denoising by wavelet method can be realized by
observing these local maximums at each scale. A commonly
used wavelet denoising method proposed by Donoho [12]
regards the wavelet coefficient below a threshold as noise and
set them to be zero.
The results of classifications should be then filtered using
median and sieve filters to remove noise and all polygons that
are smaller than a given minimum size, measured in pixels. The
774
level of filtering must be chosen adequately to both keep
small or isolated feature map lines and remove enough grid
lines and contours that may reduce the feature visibility.
Comparing the classification results using these three
different techniques. it is easy to find that the classified
images in Figure 3 and 6 using thresholding method are the
clearest. The FCM algorithm is very noise sensitive. The
images in Figure 4 and 7 present a lot of salt-and-pepper
noise. Since in this example the images are single band/ the
decision tree method is very similar to the thresholding
method. By analyzing the training data, a tree is structured
with the pixel value being the only split variable for each
node. It is like using the sample data to find the threshold and
then do the thresholding classification. The performance of
the decision tree method depends on the accurateness of the
sample data and is more sensitive to the additive noise than
the thresholding technique. Among these three methods, the
FCM algorithm is the most automatic one, which doesn't
need the training data, but at the same time, gives the worst
results.
For the multi-spectral, hyper-spectral or multi-polarized
images, classification may be done using matched filter [3].
[5-7] or matched subspace filter.
3. CREATION OF LAYERS
"Layers" can be defined as images containing part of the
information of the original image. For example, for a multi-
band image, each band can be viewed as a layer. The mean of
all the bands can be also viewed as a layer. Applying the
Principle Component Analysis (PCA) to the multi-band
image, the images generated by the principle components are
also the layers of the original image. Another example of
layers is applying the orthogonal decomposition to the
original image, the resulting orthogonal components are the
layers of the image. Saying a set of layers are "complete"
means the original image can be fully generated using this set
of layers.
The layers are generated based on the user's need. Each layer
should contain only part of the information of interested.
Normally, compared with the original image, each layer
contains less information, so it's easier to perform the
calculations, transformations based on layers. Furthermore, in
some cases, only parts of the layers are useful such as in
image fusion by PCA.
For the topographic change detection, we are interested in the
region changes for different time, so the layers we used in
this paper are based on the region classifications. Each layer
contains only one region of the original image. In Figure 6,
cach image contains three regions that are land, shallow
water and deep water. These regions should be extracted one
by one to generate the layers. Figure 9 shows the
corresponding layers of both images. The images in red are
the layers of the image taken in May, and the layers taken in
August are plotted in green. (a) and (d) are the layer-of-land
with land represented in red/green. In (b) and (c), except the
regions of shallow water, all the others are in black. So they
are the layer-of-shallow water. Similarly, (c) and (f) are the
layers-of-deep water.
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